The generator matrix

 1  0  0  1  1  1  1  1  1  1 2X^2+2X  1  X  1  1  1 2X 2X^2+2X X^2+X  1  1  1  1  1  1  1 X^2+2X  0  1 X^2  1 2X^2  1  1  1  1  1  1  1 X^2  X X^2+X  1  1  1  1  1 X^2+X X^2  1 2X  1  1 2X^2+X  1  1 X^2+X X^2+X  1  1 2X  1
 0  1  0  0 X^2 2X^2+2X+1 2X^2+2X+1 X+2  1 2X^2+X+2  1 2X^2+2  1 X^2  0 X^2+2  1  1 2X^2+2X X+2 X^2+1 X^2+X 2X+2 X^2+X+1 2X^2+X+1 2X^2+X+1  1  1 2X+1  1 X^2+2 2X^2+2X X^2+2  0 X^2+X 2X^2+2X X^2+X 2X^2+2X+1 X^2+2X+1  1  1 2X^2 2X^2+2X+2 2X+2 2X^2+X+2 X+1 X^2+X+1 2X^2+X  1 2X^2+2X+1  1 X+1  2  1 X^2+2X X^2+1  1 2X^2+X 2X^2 2X  1 2X^2+X+2
 0  0  1  1 2X^2+2 2X^2+2 2X^2+2X  1 X^2+1 2X^2+2X 2X^2+2X+1 2X^2+X+2 X^2+X+2  0 2X+2 2X^2+1 2X+1 2X^2+2X  1 X+2 X+1 X+1 X^2 X^2+2X X^2+2X+2 X^2+2X+1 2X^2+2X+2 2X^2+X+1 X+2 2X X^2+X+1  1 2X+2 2X^2+X+2 X^2+2X+2 X^2+X+1 2X^2+X 2X^2 X^2+2X X^2+2X+2 X^2+X+2  1  2  X X^2+2X 2X^2+2X+1 X+1  1 X^2 2X^2+2 X+1  2 X^2+2X+1 2X^2+2X+1 2X^2+2 X^2+1 X^2+2  1 2X^2+X+1  0  X  2
 0  0  0 2X 2X^2 X^2  0 X^2  0 2X^2  0 2X^2 X^2  X X^2 2X^2+2X 2X^2+X 2X 2X^2+X X^2+X 2X 2X^2+X X^2+2X  X 2X 2X^2+X X^2+X 2X^2+2X 2X^2+X X^2+X X^2+X 2X^2 2X 2X^2+2X  X X^2 2X^2+2X 2X X^2+X 2X^2+X 2X^2+2X X^2+2X  X 2X^2+X X^2 2X X^2+X  X  X  X 2X 2X^2  X X^2+X X^2+X 2X^2 2X^2+X X^2+2X 2X^2+X 2X^2+X  0 2X

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+708x^114+1218x^115+2610x^116+3998x^117+5940x^118+6780x^119+10024x^120+13308x^121+13218x^122+17558x^123+20436x^124+16572x^125+19058x^126+16584x^127+11004x^128+7874x^129+4974x^130+2526x^131+1516x^132+606x^133+180x^134+142x^135+84x^136+72x^137+90x^138+24x^139+6x^140+24x^141+6x^142+6x^143

The gray image is a linear code over GF(3) with n=558, k=11 and d=342.
This code was found by Heurico 1.16 in 64.2 seconds.